A Review of Surrogate-assisted Evolutionary Algorithms for Expensive Multimodal Optimization Problems

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A Review of Surrogate-assisted Evolutionary Algorithms for Expensive Multimodal Optimization Problems

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[1]JI Xinfang,JIA Jingwei,et al.A Review of Surrogate-assisted Evolutionary Algorithms for Expensive Multimodal Optimization Problems[J].Journal of Zhengzhou University (Engineering Science),2026,47(4):89-99.[doi:10.13705/j.issn.1671-6833.2026.04.014]

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Journal of Zhengzhou University (Engineering Science)[ISSN 1671-6833/CN 41-1339/T] Volume: 47 Number of periods: 2026 Issue 4 Page number: 89-99 Column: Public date: 2026-07-10

Title:: A Review of Surrogate-assisted Evolutionary Algorithms for Expensive Multimodal Optimization Problems

Author(s):: JI Xinfang^{1, 2}, JIA Jingwei^{1, 2}, WANG Xiaofeng^{1, 2}, CHENG Jinxin³, YAO Jiaxing^{1, 2}; 1. School of Computer Science and Engineering, North Minzu University, Yinchuan 750021, China; 2. The Key Laboratory of Images and Graphics Intelligent Processing of State Ethnic Affairs Commission, North Minzu University, Yinchuan 750021,China; 3. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China

Keywords:: expensive optimization problems; multimodal optimization problems; evolutionary algorithms; surrogate model

CLC:: TP18O224

DOI:: 10.13705/j.issn.1671-6833.2026.04.014

Abstract:: Expensive multimodal optimization problems (EMMOPs) arise in engineering design frequently and are often characterized as multimodal properties and with extremely high evaluation costs. The progress and key techniques of surrogate‑assisted evolutionary algorithms (SAEAs) for such problems were systematically reviewed in the study. Firstly, typical surrogate models, including polynomial regression model and Gaussian process, were introduced, with emphasis on their characteristics and applicability in sample fitting, nonlinear representation, and uncertainty quantification. Then, the general framework of SAEAs was summarized, and the main design ideas of existing algorithms were outlined in terms of single‑surrogate and multi‑surrogate structures, global‑local collaborative search, and infill sampling strategies. Subsequently, according to the different characteristics of EMMOPs, typical EMMOPs, including single‑objective, multi‑objective, constrained, and high‑dimensional problems, were systematically categorized and reviewed, with particular attention to advances in mode identification, solution diversity preservation, and computational budget allocation. Furthermore, experimental comparisons of multiple mainstream SAEAs were conducted on ten benchmark test problems, and the performance differences among various algorithms were analyzed in terms of metrics such as global optimum solution and effective valley ratio. Meanwhile, engineering case studies, including ship structure optimization and synchronous machine design in ultra‑high‑voltage direct current transmission systems, were incorporated to illustrate the application potential of surrogate‑assisted evolutionary algorithms in complex engineering optimization. Finally, the key challenges faced by current research were summarized, and future development directions were discussed from the perspectives of adaptive surrogate model management, parallel execution and scheduling, as well as inter‑modal information sharing and transfer mechanisms.

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Last Update: 2026-09-22